The Fourier-based Synchrosqueezing TransformReport as inadecuate

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1 MGMI - Modélisation Géométrique & Multirésolution pour l-Image LJK - Laboratoire Jean Kuntzmann

Abstract : The short-time Fourier transform STFT and continuous wavelet transform CWT are intensively used to analyze and process multicomponent signals, ie superpositions of mod- ulated waves. The synchrosqueezing is a post-processing method which circumvents the uncertainty relations, inherent to these linear transforms, by reassigning the coefficients in scale or frequency. Originally introduced in the setting of the continuous wavelet transform, it provides a sharp, con- centrated representation, while remaining invertible. This technique received a renewed interest with the recent publi- cation of an approximation result, which provides guarantees for the decomposition of a multicomponent signal. This paper adapts the formulation of the synchrosqueezing to the STFT, and states a similar theoretical result. The emphasis is put on the differences with the CWT-based synchrosqueezing, and all the content is illustrated through numerical experiments.

Keywords : multicomponent signals short-time Fourier transform ridge analysis synchrosqueezing reassignment

Author: Thomas Oberlin - Sylvain Meignen - Valérie Perrier -



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